The Triangle Comparison Lemma is a fundamental result in Riemannian geometry that provides a relationship between the lengths of triangles in different geometric spaces, particularly when comparing triangles in a Riemannian manifold to those in Euclidean space. This lemma allows for the comparison of the side lengths and angles of triangles, which can lead to insights about the curvature of the underlying manifold. It serves as an important tool for establishing geometric inequalities and understanding the geometric properties of spaces under various curvature conditions.
congrats on reading the definition of Triangle Comparison Lemma. now let's actually learn it.